Center of Mass Tutorial

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A green block, 1.00 kg, sits on a red block, 4.46 kg, as shown in the animation (position is in meters and time is in seconds). The all surfaces are frictionless except for the gray patches on the red block. Given the self-propelled motion of the green block, determine whether momentum and/or energy is conserved in the animation. If not, why?  Start


Well, momentum is conserved because there are no external forces. The momentum of the system was zero before the green block moves, is zero when the blocks move, and is again zero when the blocks are stationary. From the point of view of the center of mass, Vcm=0 and therefore Pcm=0.

 

We can see this by considering what happens to the center of mass during the animation.   Start  

The center of mass of the system is Xcm=(mx+mx)/(m+m) which is represented by the black dot. Note that the center of mass of the system does not move relative to the ground but does move relative to the right edge of the red block to the left, but the red block moves to the right. In fact we can look at the center of mass for each object by replacing each block by a dot as well. Start

What about energy? Well, as is always the case, it depends on how you define your system. Looking just at the center of mass, since Vcm =0 energy is conserved. However if we look at the blocks individually energy (in the sense of mechanical energy) is not conserved. Energy stored in the individual elements of the system (presumably the green block's potential energy) is turned into kinetic energy of both blocks and then is dissipated by friction. Since the force the green block exerts on the red block is equal and opposite to the force the red block exerts on the green block (Newton's Third law) when we consider the system as a whole, it does not make a net force on the center of mass system.

 

 

Animation 1

Animation 2

Animation 3